Transcript SLAB ANALYSIS, FRICTION CALCULATIONS, WORK BALANCE

SLAB ANALYSIS, FRICTION
CALCULATIONS, WORK BALANCE
SLAB ANALYSIS
• Slab analysis
–frictionless
–with friction
–Rectangular
–Cylindrical
• Strain hardening and rate effects
• Flash
• Redundant work
SLAB ANALYSIS ASSUMPTIONS
• Entire forging is plastic
–no elasticity
• Material is perfectly plastic
–strain hardening and strain rate effects later
• Friction coefficient (m) is constant
–all sliding, to start
• Plane strain
–no z-direction deformation
• In any thin slab, stresses are uniform
OPEN DIE FORGING ANALYSISRECTANGULAR PART
Expanding the dx Slice
P=die pressure
σx , dσx from material on side
Τfriction = friction force =µp
Force Balance in x-direction
Force Balance
Differentiating, and subsituting, into Mohr’s Circle Equation
Sliding Region
Forging Pressure-Sliding Region
Average Forging Pressure-Sliding
Forging Force-Sliding
Forging Pressure Approximation
Taking the first two terms of a Taylor’s series
expansion for the exponential about 0, for ΙxΙ≤1
Average Forging Pressure-All Sliding
Approximation
using the Taylor’s series approximation
Forging Force-All Sliding Approximation
Slab-Die Interface
• Sliding If:τf <τflow
• Sticking If: τf ≥ τflow
–can’t have a force on a material greater than its
flow (yield) stress
–deformation occurs in a sub-layer just within
the material with stress τflow
Sliding/Sticking Transition
Sticking Region
Forging Pressure-Sticking Region
Average Forging Pressure-Sticking
Average Forging Pressure-Sticking
Forging Force-Sticking
Forging Pressure-All Sticking Pressure
If xk << w, we can assume all sticking, and approximate the
total forging force per unit depth (into the figure) by:
Forging Pressure-All Sticking
Approximation
Average Forging Pressure-All Sticking
Approximation
Forging Force-All Sticking Approximation
Sticking-Sliding
• If you have both sticking and sliding, and you can’t
approximate by one or the other,
• Then you need to include both in your pressure and
average pressure calculations.
Why is a friction coefficient above 0.5 not
meaningful?
•The internal shear stress within the workpiece is τ = µp. The
interface pressure p is the same as the interface stress, σ.
Therefore, the internal shear stress is τ = µσ.
•From Tresca, τmax = 0.5 σ. The internal stress cannot exceed
τmax because shear will occur.
•Therefore, τ = µp = 0.5 σ = τmax. So, internal shear occurs
above m = 0.5. QED
Material Models
• Strain hardening (cold – below recrystallization
point)
• Strain rate effect (hot – above recrystallization
point)